This invention describes a safer system of control and navigation of fixed wing aircraft. This development derives its accuracy from Satellite Global Positioning Systems (GPS). The Global Positioning Systems are generated by orbiting satellites which are located high above the earth. In some instances, a combination of satellites and supplementary ground systems, such as Wide Area Navigation Systems (WAAS), Differential GPS (DGPS), and the like may be employed to improve the overall navigation accuracy. The use of GPS systems in place of the usual radar and radio methods of navigation provides greatly improved four dimensional accuracy and simplicity of derived Instrument Landing Systems (ILS). The GPS derived ILS system of the present invention results in improved and more reliable flight safety over conventional ILS systems. In addition, a plurality of conventional flight and navigational instruments are replaced by a single compound instrument which provides accurate flight information in one display which is easy to understand. The flight instruments operate without vacuum or moving parts, eliminating the primary failure mechanisms for conventional devices.
Note: When referencing to the pilot as a xe2x80x9chexe2x80x9d, it is understood that pilots can be of either sex. The terminology used, therefore, is generic in nature, and signifies any pilot.
When pilots learn to fly an aircraft, they first learn to fly by xe2x80x9cVisual Flight Rulesxe2x80x9d (VFR). Under these rules, flight is limited to those weather conditions where good visibility exists. The reliance on flight instruments is minimal. Slowly, the pilot learns to handle his aircraft and to read and to rely on the other instruments on the control panel. He learns how to mentally relate these instrument readings to what the actual aircraft is doing. For example, by looking out the window, the pilot can tell which direction is toward the ground, but he usually cannot tell if the aircraft is actually going up or going down by feel or by sight, unless the relative changes in elevation are large. People who have flown over water can attest to the difficulty of determining how far above the water the aircraft is flying. Conventionally, a vertical velocity indicator instrument tells the pilot if the aircraft is going up or down and how fast the aircraft is gaining or losing altitude. The altimeter instrument tells the pilot how high he is above sea level. Airport elevations are reported as feet above sea level, and the altimeter instrument is vital in maintaining traffic separation and when making aircraft landings.
As the fledgling pilot advances in his art, he is able to depend upon his instruments to a greater extent. The pilot develops the ability to envision the flight of his aircraft in his mind.
Eventually, after examination by his instructor, the pilot becomes certified to fly under xe2x80x9cInstrument Rulesxe2x80x9d (IFR). It is important to note that flying by instruments is not merely a convenience. Flying by instrument is actually a life-saving capability. Instruments are designed to assist the pilot in flying his aircraft in inclement weather, and under other adverse conditions. Unfortunately many pilots are intimidated by the instrument rating process and fail to learn this important flying skill.
Although the instruments eventually become the pilot""s mainstay, they can and do fail. As a result, the pilot is usually taught how to fly his aircraft with one or more instruments malfunctioning. The instructor achieves this by covering the instrument of his choice and then exhorting the pilot to fly without the selected instrument. However, instrument availability would be a preferred solution.
If, for example, inclement weather closes in, and the pilot finds himself in the clouds, with little or no visibility, the only means of control that he has over his flight is by means of the aircraft instrumentation. Safe flight is then often not possible without dependence upon navigation and control instruments. Furthermore, if there is an instrument failure while the pilot is in the clouds or in a fog, the pilot may become disoriented and such situations often prove to be fatal.
Aware of these problems, engineers have worked to improve the science of flight. In order to improve the safety of flying, engineers have developed radio and radar based instrumentation systems which enable a pilot to land his aircraft safely even when conditions are far from ideal, or when the pilot is unfamiliar with the airport at which he is attempting to land. Such systems are called xe2x80x9cInstrument Landing systemsxe2x80x9d (ILS), and they have been developed to make landing safer and to save lives. These ILS systems are replaced by the present invention which does not depend upon radio or radar navigation.
The directional and instrument landing systems which were initially developed were very primitive by today""s standards. Instrument Landing Systems (ELS) have improved steadily over the past decades. These newer systems employ radar position sensing, multiple phased arrays, radar altimeters, radio transponders, Infra red imaging, holograms and other devices. Instead of listening to a tone or series of tones, the pilot now has a cross-hair display. In most ELS systems, there is a set of xe2x80x9ccross hairsxe2x80x9d which move up or down or to the right and left to indicate where the pilot""s aircraft is located relative to the center of the xe2x80x9cbeamxe2x80x9d. This system is called a Glide Slope Indicator. By keeping the cross hairs centered in the display as he descends, the pilot knows that he is flying xe2x80x9cOn the Beamxe2x80x9d, correcting for errors in horizontal position and for errors in elevation. Thus, the pilot can execute a safe landing at a controlled airport. These systems are exemplified in the Prior Art described herein.
During the past decade, however, engineers have developed extremely accurate Global Positioning Systems (GPS). These location systems do not depend upon conventional radar or radio signals, but in their place, multiple satellites send high frequency signals to earth. These satellites are configured as a four dimensional Global Positioning System (GPS). Specialized localizers which are tuned to satellite frequencies can tell an operator precisely where and when he is on the surface of the earth with an accuracy of a few meters and less than a millisecond.
Present xe2x80x9cinexpensivexe2x80x9d GPS systems exhibit an accuracy of position of approximately 100 feet in all directions 95% of the time. WAAS and DGPS systems improve the accuracy down to the 25 foot range. Modern military GPS systems exhibit far greater accuracies. It is anticipated that the present invention will be able to be enhanced as more accurate GPS systems become available to the general public.
It is well known to those who fly, that modem GPS systems are very accurate. These systems are rapidly replacing LORAN and other systems which are presently used for navigation, but do not provide altitude information.
The present invention, which the inventor calls a xe2x80x9cVirtual Instrument Pilotxe2x80x9d utilizes the aforementioned Global Positioning Systems to tell the pilot precisely where he is located with respect to actual spatial positions on the surface of the earth and in the air. The present invention, however, goes further than simply using the GPS as a navigational aid. The system described herein uses the GPS as an input source by which a complete functional aircraft control system can be accomplished in a single unified instrument and displayed upon a single display, which is readily understood by the pilot.
The reliability of the present invention stems from the avoidance of any moving parts or parts which are exposed to the environment during data acquisition. The data input is also isolated from the rest of the aircraft instrumentation. The present invention provides the equivalent of most of the needed flight instruments for Attitude determination, navigational Aids, and route control functions of modern avionics in a single, reliable instrument. This minimizes the instrument visual scan by the pilot that is presently required with separate units. A partial list of functional items normally found in separate flight instruments follows. These are:
A) Aircraft attitude indicator, including an artificial horizon and aircraft model showing both bank and pitch angles.
B) Aircraft turn rate showing the rate relative to a standard (2 minute) turn in either direction.
C) Sensitive altimeter
D) Vertical velocity indicator
E) Compass
F) Air Speed indicator (Not instantaneous)
G) Blind altimeter (not on control panel, used by transponder)
The following instruments are found in aircraft navigational aids:
H) Distance from any established system or user defined navigational aid.
I) Bearing to any established system or user defined navigation aid.
J) Angular position relative to a specified bearing from any system or user defined navigation aid.
K) Ground speed.
L) Direction of flight.
M) Indication of deviation from pilot entered air speed and heading.
N) Calculation of wind vector from pilot entered air speed and heading.
O) Flight path determination from pre-stored data.
Additional functionality new in this system.
P) Calculation of wind vector from a simple maneuver without pilot input.
Q) Most functions (except connections to transponder and autopilot) are available in a portable unit which can be moved from one aircraft to another.
R) Ability to xe2x80x9clearnxe2x80x9d a runway. It is important to note that half of the 10,000 airports in this country are private and may not be on charts. The present invention will learn about a new airport runway by simply taking off from that runway. Once learned, the present invention will provide both pattern entry and ILS information to the pilot.
The present invention, therefore:
1) Provides the most needed flight indicators such as Attitude, Navigational Aids, and Route control functions of modern avionics are vested in a single, reliable instrument. This minimizes the instrument scan required by the pilot that is presently required with separate units.
2) The pilot has an accurate indication of his altitude and aircraft banking;
3) The instrument can replace many of those instruments currently required for flight management.
4) In an emergency, a simple xe2x80x9cPanic Buttonxe2x80x9d depression can cause the aircraft to recover to straight and level flight either automatically or via simple commands to the pilot. This feature is intended to recover an aircraft in which the pilot is hopelessly disoriented due to fog, inclement weather, or confusion.
5) From the invention display, the pilot knows what his ground speed is, and where his direction and flight path is relative to pre-defined locations (airports) or pre-entered flight paths;
6) The pilot can set or have the wind vector; calculated by the integral computer.
7) The pilot knows where he is located relative to previously selected travel plans;
8) The pilot can select and activate his flight path;
9) The present invention can be adapted to any fixed wing aircraft, has been designed to be portable, and can easily be moved from one aircraft to another.
When paired with a WAAS or DGPS sensor, the present invention is capable of replacing the functionality in normal flight of the following standard instruments: Attitude indicator, Sensitive altimeter, Rate of climb indicator, Gyrocompass, Rate of turn indicator, Compass (Both Analog and digital presentations of compass heading are displayed.), and Clock.
In this invention, the compass never has to be adjusted for drift, and the compass accuracy is not affected by any metal in the aircraft. The compass shows the direction of travel rather than the aircraft heading, and the compass accuracy is not affected by wind speed. In addition, the compass reading is presented to the pilot in a digital readout, eliminating the need for interpolation.
While there are many devices in the marketplace that perform various combinations of the functions enumerated herein, there are no instruments in which all of the functions are incorporated in a single unit.
When turned on, the invention provides simultaneous navigational information for marker beacons and up to three navigational aids. The instrument of the present invention will direct the pilot through maneuvers needed to execute preplanned flights, and landing patterns. The display of the present invention also shows an artificial horizon which differs from the conventional display in that the horizon is placed above or below cross hairs which represent the direction of flight rather than the pitch of the aircraft. The pitch of the aircraft can be seen by observing the height of the airplane figure above the artificial horizon. In this way, the pilot has an improved visual indication of whether he is climbing or descending.
An additional feature of the present invention is that the invention is also an integrated Instrument Landing System, displaying the conventional outer, middle, and inner marker beacon indicators. Virtual ILS indications are provided for runways which do not have an ILS system. These function in the normally expected manner and are used to indicate the necessary marker beacons and missed approach points, which the pilot is expecting to find in flight.
One other advantage of the Virtual Instrument Pilot is that conventional instruments rely upon the change in barometric pressure to tell the pilot when there is a change in vertical velocity. In these mechanical systems, the change is not reported for a period of between 6 to 9 seconds. In the Virtual Instrument Pilot of the present invention, the lag in vertical velocity readout is typically 1.5 to 3 seconds.
All of these functions are accomplished in an instrument can continue to function for an hour or more if all of the electrical and vacuum power in the aircraft fails.
One of the major advantages of the present invention is that it contains virtually all of the necessary instrumentation required to safely fly and navigate an aircraft anywhere in the world. These instruments are embodied in one convenient and independent package. The Virtual Instrument Pilot can function completely independent of the aircraft vacuum and power systems. In the event of a complete battery failure, the aircraft can continue to fly because the engines receive ignition energy from the engine magnetos. In the absence of all power, the Virtual Instrument Pilot of the present invention can continue to operate for a minimum of an hour on its own internal pre-charged batteries. The internal batteries are on continuous float charge while normal DC power is available. A transition-free connection to the internal batteries is made if normal power fails.
The system of the present invention can also automatically notify the pilot where he is, hat his latitude and longitude are, how far off course his aircraft is, and what his next heading is to be. If a pilot simply takes off from a new airport which is not in his database, the Virtual Instrument Pilot of the present invention xe2x80x9clearnsxe2x80x9d to identify the airport which the pilot took off from, and the data is remembered and can be downloaded into another computer at the end of the flight.
As noted earlier herein, if inclement weather closes in, and the pilot finds himself in the clouds, the only means of control that he has over his flight is by means of the aircraft instrumentation. Safe flight often then becomes impossible without dependence upon navigation and control instruments. Furthermore, if there is an instrument failure while the pilot is in the clouds or in a fog, the pilot may become disoriented and such situations can prove to be fatal. Very experienced pilots have been known to crash under these conditions. The present invention has been designed to eliminate and prevent such crashes.
The present invention, which is called a xe2x80x9cVirtual Instrument Pilotxe2x80x9d, utilizes the aforementioned Global Positioning Systems to tell the pilot precisely where he is located with respect to known airports. The present invention will also tell the pilot which direction he is flying, what his altitude is, what his ground speed is, what his bank angle is, what his pitch is, and where his position is relative to pre-defined locations (airports), and where he is located relative to previously selected travel plans. Wind vectors are computed from either manual input of airspeed and heading of after a simple circular maneuver is executed.
One of the major advantages of the present invention is that it contains most of the necessary instrumentation required to safely fly and navigate an aircraft, and can function completely independent of the aircraft vacuum and power systems.
The present invention continually indicates the aircraft position over the surface of the earth (including over the seas). The invention can automatically tell the pilot how far off course his aircraft is, where his next heading is to be, and how to move his controls in order to restore his aircraft to the pre-determined flight path. This information only partially available on present navigation and ILS systems.
Although this invention has been shown and described with respect to detailed embodiments thereof, it will be understood by those skilled in the art that various changes in form and detail may be made without departing from the spirit and scope of the claimed invention.
The primary object of the invention is to provide clear, easy to understand flight information to the pilot and to aid in a safe and efficient flight. A major object of this invention, therefore, is that; while using the Global Positioning System (GPS) as a source of continuous data, The Virtual Instrument Pilot can derive the following flight functions directly or by *mathematical computation: Latitude, Longitude, Altitude, Time, ground speed, vertical velocity, direction of travel, aircraft bank, aircraft pitch, wind vector, air speed, distance from a navigational reference, bearing to a navigational reference, relative direction of omni-bearing from navigational references, vertical and horizontal position along a glide path, physical maneuver to achieve destination at a specified altitude-speed-direction, and the control motion required to achieve the desired flight path.
All of the above indicators of flight are derived without the use of xe2x80x9cconventionalxe2x80x9d mechanical, electrical, or vacuum operated instruments.
It is another object of the invention to provide an improved approach for the pilot and/or autopilot enabling the pilot to make a safe landing under unusual flying conditions.
It is a further object of this invention to reduce the effects of disorientation, which often occurs with conventional instrumentation, by replacing these instruments with a single unified instrument having attitude, position, and command information immediately and continuously visible. The graphical command information will guide the pilot""s actions until he has regained his orientation. The ease of this operation is described herein.
Pilots must be able to deviate from the pre-planned path due to traffic control, weather or other difficulties. Current non-directional Beacons (NDB) are not expected to phase out until the year 2005, and Vector Omni Range (VOR/Distance Measuring Equipment (DME) are not expected to be phased out until the year 2010. Rather than eliminate current instrumentation, the system will also incorporate all of the instrument functions which are described herein In a single unified display.
Another object of this invention is to provide a navigation and control device which is free from failure due to mechanical, environmental, or power source factors. Units that are powered by vacuum systems are prone to failure due to corrosion if moisture gets into the system. Units that are powered by the electrical system usually fail when power is lost.
Instrument failures can be dangerous. For example, if the attitude indicator fails or xe2x80x9ctumblesxe2x80x9d, the pilot must determine the aircraft""s attitude from a number of other instruments. The loss of the attitude indicator and the resulting disorientation present a real danger of loss of life. In addition, autopilots obtain feedback information from the vacuum operated attitude indicator, and the autopilot could react violently to a failed attitude indicator, with the potential for an uncontrollable crash of the aircraft.
The invention will provide a unique approach to directing the pilot and dealing with disorientation. Much has been done in recent years to deal with this problem. Most approaches involve trying to make the instrument view of the flight situation as xe2x80x9crealxe2x80x9d as possible so that someone with less ability for spatial relations will more easily see and be able to correct the situation. While that approach might help, this invention intends to bypass the interpretation problem. The pilot will be presented with a direct solution to control and navigation of the aircraft, telling him or her which way and how much to move the controls in order to achieve the desired flight path correction.
It is a farther object of this invention whereby should the pilot become disoriented, the simple press of a single button will activate directions to the pilot (or autopilot) for the correct maneuver to return the aircraft to straight and level flight. A pilot who experiences a complete loss of visibility due to fog or other impediment, can xe2x80x9crightxe2x80x9d his aircraft by simply pressing a panic button. If autopilot equipped, the system of the present invention will take over control of the aircraft. If not, the present invention will present easily understood simple graphical instructions to the pilot for immediate flight correction. The aircraft will be righted and be set on a straight and level path.
Another object of the invention is to provide explicit and easy to understand directions for standard Instrument Flight Rules (IFR) and Visual Flight Rules (VFR) approaches to airports, for holding patterns, for pilot defined flight paths, for standard search and rescue patterns, for paths that are pre-defined in flight, or for pre-loaded user defined flight paths.
Another object of the invention described herein is to learn the necessary information about the flight from data gathered by the Virtual Instrument Pilot during flight. The present invention is capable of xe2x80x9clearningxe2x80x9d a new airport simply from data gathered during takeoff by the pilot.
Another object of the invention is to keep the computer architecture open, allowing for other systems to utilize the same hardware and display. Control panel clutter reduction is another major goal of this invention. In general, where desired, total redundancy can be achieved by installing two units in an aircraft. By sharing the hardware resources with other products that could be turned off if a system fails, we eliminate waste and keep the control panel simple.
It is an object of the present invention to provide a safer system for navigation and control of a fixed wing aircraft which is based upon the use of orbiting satellites, deriving flight information from a Global Positioning System.(GPS), Wide Area Augmentation System (WAAS), or from Differential Global Positioning System (DGPS).
Another object of the invention is to provide an improved Instrument landing System (ILS) in which spatial locations are derived without the use of conventional radar, radio, or standard communication methods. After the airport data is entered into the onboard computer, or the airport data is learned by the system, the pilot can find his way back to the airport and approach landing there, by utilizing the internal navigational and ILS system aids of the present invention.
Another object of the invention is to provide an instrument employing a single unified display which tells the pilot all the information that he requires to achieve safe flight. The reduction of panel clutter is an important improvement in flying.
Another object is to provide a single instrument which serves as an Instrument landing system, a glide slope indicator, a global positioning system, and a flight controller.
Another object of the invention is to provide a navigation and control system which can function if all of the electrical power and vacuum power on the aircraft fails. Operation, of the Virtual Instrument Pilot will be powered by internal batteries which will be functional for a minimum of one hour after a complete power failure. It is expected that within one hour, the pilot can locate and land his disabled aircraft at an airport where he can obtain the needed assistance to correct his aircraft failure.
A major object of this invention, defined earlier, is that; by using the Global Positioning System (GPS) as a source of continuous data, we can derive the following flight functions directly by mathematical computation based solely upon the derived data: Latitude, Longitude, Altitude, Time, ground speed, vertical velocity, direction of travel, aircraft bank, aircraft pitch, wind vector, air speed, distance from a navigational reference, bearing to a navigational reference, relative direction of omni-bearing from navigational references, vertical and horizontal position along a glide path, physical maneuver to achieve destination at a specified altitude-speed-direction, and the control motion required to achieve the desired path.
The necessary mathematical equations to solve the above elements during flight are included in the Best Mode for carrying out the invention.
There are very many patents which relate to aircraft management and control. Some of the more relevant specimens of recent prior art are indicated here. Old prior art appears not to be relevant to this application, due to advances in instrumentation technology.
U.S. Pat. No. 4,209,768 issued to Basov et al. On Jun. 24, 1980. AIRCRAFT TAKE-OFF AND LANDING SYSTEM AND METHOD FOR USING SAME. This patent describes the use of pencil-thin electromagnetic radio beams which are directed to assist takeoffs and landings of aircraft.
U.S. Pat. No. 6,119,055 issued to Richman on Sep. 12, 2000 REAL TIME IMAGING SYSTEM AND METHOD FOR USE IN AIDING A LANDING OPERATION OF AN AIRCRAFT IN OBSCURED WEATHER CONDITIONS. This patent comprises a CCD camera located on the aircraft and a plurality of synchronized radiant energy sources and LED assemblies located adjacent to the airport. A processor digitally filters information which enhances the view of the aircraft landing area. Additionally, there are LED assemblies located on an aircraft mounted display. These LED""s represent the topology of the runway on the ground, thus providing a simulated image of the runway which is heretofore invisible to the pilot due to obscuring weather. The system is a visual aid to performing a landing procedure in inclement weather.
U.S. Pat. No. 6,112,141, issued to Briffe et al on Aug. 29, 2000 APPARATUS AND METHOD FOR GRAPHICALLY ORIENTED AIRCRAFT AND CONTROL. In this invention, a plurality of flat panel displays are utilized to represent the flight patterns of known aircraft. Separately identifiable cursors are used to manipulate aircraft flight paths, and the system may be engaged to control the flight paths of known aircraft in order to maximize flight safety.
U.S. Pat. No. 6,057,786 issued to Brife et al, on May 2, 2000 APPARATUS AND METHOD FOR AIRCRAFT DISPLAY AND CONTROL INCLUDING HEADS-UP DISPLAY. This invention the pilot can view his flight information by looking through the aircraft window. He obtains information on aircraft velocity vector, desired aircraft velocity, acceleration, and pitch. The on board computer generates a waypoint icon in the path of view of the geographic location and altitude of the actual way point.
U.S. Pat. No. 6,031,488 Issued to Hua et al, on Feb. 29, 2000 METHOD AND SYSTEM FOR AN EFFICIENT LOW COST PPS GPS RECEIVER This invention describes a system for using Precise Positioning Service signals from a Global Positioning System . A second GPS system is also used to analyze the data to obtain positioning data.
U.S. Pat. No. 5,945,943 Issued to Kalafus et al, On Aug. 31, 1999. SYSTEM FOR USING DIFFERENTIAL GPS RECEIVERS WITH AUTOPILOT SYSTEMS FOR CATEGORY III PRECISION APPROACHES. The referenced invention describes the use of a plurality of Differential Global Positioning receivers (DGPS) to obtain information which can be used for precision landing data.
This invention is a complete system which will provide continuous graphical directions to the pilot of an aircraft to enable him to fly pre-defined flight paths. For paths which have not been entered into the system, the presentation of more traditional instruments may be utilized. The invention described herein, which is embodied in a single graphical display, will partially or fully replace the standard instrument functionality, as shown in table 1. It is important to note that all instrumentation is derived from a Global Positioning System, computation of derived data, and is totally independent of conventional instrumentation which is powered by the aircraft battery system and aircraft vacuum systems. Failure of the aircraft power and vacuum systems will not have any effect on the present invention, which can operate for an hour or greater upon failure of the aircraft power or vacuum systems.
The following mnemonic abbreviations are used in this specification, and are known to all pilots.
The foregoing and other features of the present invention will become more apparent from the following description and accompanying drawings.
FIG. 1 shows a diagram of the hardware architecture of the system. The current system contains all of the functions that are shown.
FIG. 2 illustrates the Instrument Display in the present system with all optional elements turned off. For the sake of brevity and simplicity, the figure is repeated in the next two illustrations. Only the graphical elements that change due to flight are numerically illustrated in this figure.
FIG. 3 is the same Instrument Display as FIG. 2. The alphanumeric elements that change due to flight are numerically illustrated.
FIG. 4 is the same Instrument Display as FIG. 2. The static graphic elements, most of which may be modified by adaptation, and the system control alphanumeric elements are numerically illustrated.
FIG. 5 illustrates the basic Flight Instrument Display with optional navigation aids activated. The navigation aids are numerically illustrated. In this figure, they include the xe2x80x9cAimxe2x80x9d figure, one Vector Omni Range (VOR) (A), and two Automatic Direction Finders. (ADF) (BandC).
FIG. 6 illustrates the Navigation Display in the present system. In most applications, this display is located directly under the Instrument Display of FIGS. 2, 3, and 4 for the economic advantage of sharing a display screen. However, there is no reason that it could not be placed separately in a more convenient location.
FIG. 7 illustrates the switch and dial panel in the present system. In a commercial version of the present system, this software prototype of the panel will be replaced by a hardware equivalent.
FIG. 8 shows the geometric construction used to calculate the four possible direct segments between two snapshots. The label CW stands for a clockwise arc. The label CCW stands for a counter-clockwise arc. The entry and exit points are indicated by dots near their associated arrows. The small triangle in each arc circle represents the delta angle that is described in the text. FIG. 8 is provided to illustrate the in flight derivation of physically realizable flight paths between an entry and exit snapshot. A snapshot is defined as the position, time, speed and direction of an aircraft. A direct segment consists of two arcs connected by a straight line. Four snapshot to snapshot segments are shown as (a), (b), (c), and (d).
FIG. 9 shows the projection performed to derive a route segment from a direct segment. A route segment provides a shortened maneuver to position an aircraft on a specified linear path followed by travel along that path. A route segment is derived from a direct segment in FIG. 8 by moving the exit arc opposite to the exit direction and inserting an additional line element following the exit arc leading up to the exit snapshot.